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Describe about Arithmetic and Geometric Series?
When the terms of a sequence are added together instead of separated by commas, the sequence becomes a series. You will use series in higher mathematics. Example 1: 3 + 6 + 9 + 12 + ...The pattern is add three to the previous term. When the pattern is to always add or subtract the same number, you have an arithmetic series. Example 2:1 + 2 + 4 + 8 + ...The pattern is multiply two to the previous term. A series that has a pattern of multiplying or dividing by the same number is called a geometric series.
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Determine an actual explicit solution to y′ = t/y; y(2) = -1. Solution : We already identify by the previous illustration that an implicit solution to this IVP is y 2 = t 2 -
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The tenth term in the binomial expansion of (1-1/4)(1-1/5)(1-1/6)...(1-1/n+3) is equal to
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